Right, the environments are not uniformly distributed. In fact, the paper actually defines not one single intelligence comparator but an infinite family, parametrized by a hyperparameter which is, essentially, a choice of which environments vote and how to count their votes. Crucially, this doesn't change the truth of the structural theorems (except that some of the theorems require the hyperparameter satisfy certain constraints).
Other authors (Legg and Hutter, 2007) followed the line of reasoning in your comment much more literally. They proposed to measure the intelligence of an agent as the infinite sum of the expected rewards the agent achieves on each computable environment, weighted by 2^-K where K is the environment's Kolmogorov complexity. Which seems as if it gives "one true measure" of intelligence, but actually that isn't the case at all, because Kolmogorov complexity depends on a reference universal Turing machine (Hutter himself eventually acknowledged how big a problem this is for his definition, Leike and Hutter, 2015).
My position is that any attempt to come up with "one true comparison of intelligence" (as opposed to a parametrized family) should be viewed with skepticism, because relative intelligence really must depend on a lot of arbitrary choices.
Other authors (Legg and Hutter, 2007) followed the line of reasoning in your comment much more literally. They proposed to measure the intelligence of an agent as the infinite sum of the expected rewards the agent achieves on each computable environment, weighted by 2^-K where K is the environment's Kolmogorov complexity. Which seems as if it gives "one true measure" of intelligence, but actually that isn't the case at all, because Kolmogorov complexity depends on a reference universal Turing machine (Hutter himself eventually acknowledged how big a problem this is for his definition, Leike and Hutter, 2015).
My position is that any attempt to come up with "one true comparison of intelligence" (as opposed to a parametrized family) should be viewed with skepticism, because relative intelligence really must depend on a lot of arbitrary choices.